Generate a rule from a patternArthimetic sequences

Numbers written in a specific order can form a sequence. Terms in a sequence can be related by patterns such as a common difference. Sequences where terms have a common difference are called 'arithmetic sequences.'

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Arthimetic sequences

An arithmetic sequence is one where the difference between one term and the next is always the same.

For arithmetic sequences, to go from any term to the next the rule is to always add or subtract the same value.

The number added (or subtracted) at each stage (i.e the rule) of the arithmetic sequence is called the common difference.

How to work out the next term in a sequence

Step 1

  • write out your sequence:
  • 8, 11, 14, 17...

Step 2

  • find the common difference (the difference between each pair of numbers)
  • write it down:
  • 8 (+3) 11 (+3) 14 (+3) 17...

Step 3

  • use the common difference to find the next number in the sequence:
  • 17 (+3) = 20

Question

Now try steps 1-3 on a new arithmetic sequence:

70, 60, 50, 40 ...

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